1. Field of the Invention
The present invention relates to apparatuses and methods for stabilizing a carrier-envelope phase of a laser pulse. More particularly, the present invention relates to apparatuses and methods for stabilizing the carrier-envelope phase of a laser pulse by using a direct locking method.
2. Description of the Related Art
Since late 1990s, the carrier-envelope phase (CEP) stabilization of femtosecond laser pulses has been intensively studied as a key technique for high-precision frequency metrology and attosecond science. The CEP stabilization technique in mode-locked femtosecond lasers was first proposed by ultrafast laser scientists and experimentally realized by frequency metrology researchers.
Recently, the CEP stabilization technique was successfully extended to chirped-pulse amplification (CPA) laser systems for the generation of high energy and high-intensity CEP-stabilized pulses. The CEP-stabilized laser has become a revolutionary light source for the frequency metrology, whereas the CEP-stabilized CPA lasers have become an essential tool for the generation of reproducible attosecond XUV pulses that can probe ultrafast electron dynamics in atoms and molecules.
For reliable applications of the CEP stabilization technique, low phase noise and excellent long-term stability are crucial, so great efforts have been made for the enhancement of these parameters in the CEP stabilized femtosecond lasers.
As the technique for reducing pulse width of a laser pulse rapidly develops, a mode-locked pulsed laser has been developed. According to the mode-locked pulsed laser, a laser pulse width corresponds to only two laser oscillation wavelengths to reduce pulse width. Regarding the mode-locked pulsed laser, the technique for reproducing a pulse shape attracts many people's interest.
FIG. 1 shows a pulse train generated by a mode-locked pulsed laser. Referring to FIG. 1, the mode-locked pulsed laser oscillates as a pulse train shape according to a time. A time interval τ means a round trip time required for coming and going in a laser cavity. In other words, the time interval τ is represented as 2 L/c, wherein L is a length of the cavity and c is a speed of light. The time interval τ equals to the reciprocal of a repetition rate frep.
The phase difference between a peak of the carrier wave of a laser pulse and a peak of envelope is referred to as the CEP. That is, the CEP is the phase difference between a peak of the carrier wave of a laser pulse and a peak of an envelope.
According to the mode-locked pulsed laser's pulse shape, the envelopes of the laser pulses in the laser cavity do not vary as shown in FIG. 1. However, a group velocity and a phase velocity of the pulses vary due to dispersion in the laser cavity, so that peaks of the envelope of the laser pulses and peaks of the carrier waves of the laser pulses vary at every times, so that absolute phases of the laser pulses vary as φ1, φ2, φ3 and φ4 in accordance with time.
In FIG. 1, the respective CEP of the laser pulse is φ1, φ2, φ3 and φ4, respectively and a phase difference between the laser pulses is carrier-envelope phase offset (CEO), which is Δφcep. When the CEO is zero, all of the CEP generated by mode-locked pulsed laser has a same value. When the CEO is π/4, every eighth CEP has a same value.
FIG. 2 shows laser pulses having changing CEP in a time domain when the CEO has a constant value, and FIG. 3 shows laser pulses having changing CEP in a frequency domain when the CEO has a constant value.
Referring to FIG. 2, light frequency of laser pulses in the frequency domain of FIG. 3 are shifted from the position (represented by dotted lines) corresponding to multiples of repetition rate freq by the amount of the carrier-envelope offset frequency δ (or fceo) due to the constant CEO Δφcep.
In the conventional mode-locked pulsed laser, the CEO is not constant. In other words, the CEO is variable while the laser pulses are generated. Therefore, the laser frequency of the conventional mode-locked pulsed laser varies and is unstable.
According to a method disclosed in U.S. Pat. No. 6,724,788 (METHOD AND DEVICE FOR GENERATING RADIATION WITH STABILIZED FREQUENCY) of Dr. Hänsch, who is a Nobel Prize winner of 2005, and U.S. Patent Publication No. 2004/0017833 (MODE-LOCKED PULSED LASER SYSTEM AND METHOD) of Dr. John L. Hall who is also a Nobel Prize winner of 2005, the laser frequency is stably controlled by controlling the CEO. Thanks to the evolutionary laser frequency stabilizing technique disclosed in the above U.S. Pat. No. 6,724,788 and U.S. Patent Publication No. 2004/0017833, a precision of measuring time, space and mass has been thousands of times enhanced, and a measuring method has been simplified.
For example, thanks to the CEP stabilization technique, a clock having precision of down to eighteen decimal places and having only one second error throughout the age of the universe of about fourteen billion years can be obtained.
Recently, the CEP stabilization technique has been applied to fields other than physics so as to generate an atto-second (10−18 second) pulse. When an ultra-short pulse is applied to gas so as to generate plasma, a shape of laser oscillation is changed at every time, so that an amount of generated plasma is changed due to the effect of CEP. Therefore, a special light such as the atto-second pulse may be generated in the plasma by controlling the CEP. That is similar to generating ultrahigh speed flash lamp capable of taking a picture in an ultrashort time. Through this technique, a motion picture of electron in an atom may be taken. According to a method disclosed in 2003 through the Journal of ‘Nature’, the laser controlled by CEP is applied to gas, plasma is generated and then atto-second pulse is obtained, and a moving picture of electron in an atom was taken by using the atto-second pulse. After that, many researches have been performed throughout the world.
The CEP stabilization techniques disclosed in the above U.S. Pat. No. 6,724,788 and U.S. Patent Publication No. 2004/0017833 are based on the phase-locked loop (PLL) that stabilizes a CEP offset frequency so as to follow ward a reference RF signal.
The CEP stabilization techniques disclosed in the above U.S. Pat. No. 6,724,788 and U.S. Patent Publication No. 2004/0017833 stabilizes only the CEO Δφcep to have a constant value in order to stabilize a laser frequency but does not allow the CEP to have a constant value.
Therefore, as shown in FIGS. 2 and 3, the laser frequency is shifted in the frequency domain by an amount of the CEP offset frequency δ due to the CEO Δφcep.
That is, according to the CEP stabilization techniques disclosed in the above U.S. Pat. No. 6,724,788 and U.S. Patent Publication No. 2004/0017833, the CEP of the laser pulses are changed at every times, so that the laser pulse shapes in time domain are different from each other. As a result, only pulses having the same CEP should be selected in the various laser pulses, when a laser plasma experiment is performed.
Recently, in the thesis “Novel method for carrier-envelope phase stabilization of femtosecond laser pulses” disclosed on Apr. 18, 2005 through the journal of ‘OPTICS Express’, a CEP stabilization technique based on a direct locking (DL) method is proposed to replace the CEP stabilization technique based on the conventional PLL method.
The DL method has special features in comparison with the conventional PLL method. First, the reference RF signal is not required since the feedback signal is generated in the time domain from f-to-2f beat signal by using a simple DC reference. Therefore, an electronic circuit for embodying the DL method becomes relatively simple. Second, the CEP changes is locked to be zero. Third, the CEP value may be intuitionally and simply modulated in electronic ways by using a shaped external signal.
However, in spite of the advantages described above, the CEP distortion induced by a detection balancing process for removing a background DC noises may be generated when the DL is set up. Additionally, a slow drift of a feedback signal may have influence on an output of a laser pulse to generate crosstalk between the output of the laser pulse and the CEP offset frequency δ or the CEP. Therefore, a circulation ring of a feedback may be broken to disturb the CEP stabilization in the long term.